Factors and Multiples: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

18 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

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1.11DB Factors and Multiples: Fluency and Exam Drill (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 45 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write down all the even factors of 60.

(Total for Question 1 is 1 mark)

Work out the smallest multiple of 11 that is greater than 100.

(Total for Question 2 is 1 mark)

Decide whether the statement "every prime number is odd" is true or false. Give a reason for your answer.

(Total for Question 3 is 1 mark)

Given that the highest common factor (HCF) of 9 and 12 is 3, work out the lowest common multiple (LCM) of 9 and 12.

(Total for Question 4 is 2 marks)

Show that 108 = 2² x 3³.

(Total for Question 5 is 2 marks)

List all the common factors of 48 and 72.

(Total for Question 6 is 2 marks)

A gardener has 96 tulip bulbs and 72 daffodil bulbs. She wants to plant them in rows, with the same number of bulbs in every row, using only one type of bulb per row and no bulbs left over. Work out the greatest possible number of bulbs in each row.

(Total for Question 7 is 2 marks)

Write 60/84 in its simplest form. Show how you used the highest common factor of 60 and 84 to simplify it.

(Total for Question 8 is 2 marks)

The numbers 36, 44, 54, 68 and 90 are written on cards.
Sort the cards into two groups: multiples of 6, and numbers that are not multiples of 6.

(Total for Question 9 is 1 mark)

Show that 41472 is divisible by 8.

(Total for Question 10 is 2 marks)

Paper cups are sold in packs of 15. Paper plates are sold in packs of 40. Priya wants to buy exactly the same number of cups as plates for a party, with none left over. Work out the smallest number of cups (and the smallest number of plates) she could buy.

(Total for Question 11 is 2 marks)

The diagram shows part of a factor tree for 168: 168 splits into two branches, 8 and a box marked with a question mark. The branch showing 8 splits further into three boxes: 2, 2 and 2. The box marked with a question mark splits into two boxes: 3 and 7. Work out the number in the box marked with a question mark, and use it to write 168 as a product of its prime factors.

Figure (to be drawn): A factor tree with 168 at the top. 168 branches down to two boxes: 8 (left) and a box marked with a question mark (right). The 8 box branches down to three boxes: 2, 2 and 2. The question-mark box branches down to two boxes: 3 and 7.

(Total for Question 12 is 2 marks)

A student's working to find the lowest common multiple of 8 and 20 is shown below.
Line 1: 8 = 2 x 2 x 2
Line 2: 20 = 2 x 2 x 5
Line 3: LCM = 2 x 2 x 5 = 20
Identify which line contains an error, and write down the correct value of the LCM.

(Total for Question 13 is 2 marks)

Two positive integers have HCF 8 and LCM 240. One of the integers is 48. Work out the other integer.

(Total for Question 14 is 3 marks)

Three warning lights flash at regular intervals: the red light every 15 seconds, the amber light every 20 seconds and the green light every 24 seconds. All three flash together at exactly 9:00:00 am. Work out the time when all three will next flash together.

(Total for Question 15 is 2 marks)

A patio measuring 168 cm by 210 cm is to be covered exactly with square paving slabs, using whole slabs only and no cutting. Work out the side length of the largest possible square slab, and the number of slabs needed to cover the patio.

(Total for Question 16 is 3 marks)

Show that the lowest common multiple of 12, 18 and 45 is 180.

(Total for Question 17 is 2 marks)

How many positive integers less than 150 are divisible by exactly one of 3 or 5 (that is, divisible by 3 or by 5, but not both)? Show your working.

(Total for Question 18 is 3 marks)

Mark scheme · 1.11DB Factors and Multiples: Fluency and Exam Drill (Part 2)

Question 1

B1 All even factors listed: 2, 4, 6, 10, 12, 20, 30, 60 cao
Answer: 2, 4, 6, 10, 12, 20, 30, 60 (any order accepted)

Question 2

B1 110 cao
Answer: 110

Question 3

B1 False, with 2 identified as a prime, even counter-example cao
Answer: False, because 2 is a prime number and 2 is even.

Question 4

M1 Uses the relationship LCM = (9 x 12) / HCF (oe)
A1 36 cao
Answer: 36

Question 5

M1 Correct factor tree or repeated division shown (e.g. 108 / 2 = 54, 54 / 2 = 27, 27 / 3 = 9, 9 / 3 = 3)
A1 2² x 3³ = 4 x 27 = 108, so shown cso
Answer: Shown: 108 = 2² x 3³, since 2² x 3³ = 4 x 27 = 108.

Question 6

M1 Correct method: list factors of 48 and 72, or find HCF(48,72) = 24
A1 1, 2, 3, 4, 6, 8, 12, 24 cao
Answer: 1, 2, 3, 4, 6, 8, 12, 24 (any order)

Question 7

M1 Correct method to find HCF of 96 and 72 (e.g. prime factors or repeated subtraction)
A1 24 cao
Answer: 24 bulbs per row

Question 8

M1 Finds HCF(60,84) = 12 (method shown)
A1 5/7 cao
Answer: 5/7

Question 9

B1 Multiples of 6: 36, 54, 90; not multiples of 6: 44, 68 cao (all five correctly sorted)
Answer: Multiples of 6: 36, 54, 90. Not multiples of 6: 44, 68.

Question 10

M1 Uses the divisibility test for 8: a number is divisible by 8 if its last three digits are divisible by 8, and identifies the last three digits as 472
A1 472 = 8 x 59, so 41472 is divisible by 8 cso
Answer: 41472 is divisible by 8, since its last three digits (472) equal 8 x 59.

Question 11

M1 Finds LCM of 15 and 40 (method shown)
A1 120 cao
Answer: 120 cups and 120 plates

Question 12

M1 Missing branch value found: 168 / 8 = 21 (oe)
A1 168 = 2³ x 3 x 7 cao (allow 2 x 2 x 2 x 3 x 7)
Answer: The missing box shows 21; 168 = 2³ x 3 x 7.

Question 13

M1 Line 3 identified as the error: the highest power of 2 seen is 2³ (from 8), not 2², so 2³ should have been used (oe)
A1 40 cao
Answer: Line 3 contains the error; the correct LCM is 40.

Question 14

M1 Uses the property that the product of two integers equals HCF x LCM (oe)
M1 Substitutes to find the other integer = (8 x 240) / 48 (oe)
A1 40 cao
Answer: 40

Question 15

M1 Finds LCM of 15, 20 and 24 (method shown)
A1 9:02:00 am cao (accept 120 seconds or 2 minutes after 9:00:00 am)
Answer: 9:02:00 am (120 seconds later)

Question 16

M1 Finds HCF of 168 and 210 (method shown)
A1 Side length 42 cm cao
A1 20 slabs cao, ft from their side length: (168 / their side) x (210 / their side)
Answer: Side length 42 cm; 20 slabs needed.

Question 17

M1 Prime factorises all three: 12 = 2² x 3, 18 = 2 x 3², 45 = 3² x 5
A1 Takes the highest power of each prime and multiplies: 2² x 3² x 5 = 180 cso
Answer: 180 (shown: 2² x 3² x 5 = 180)

Question 18

M1 Counts multiples of 3 and of 5 up to 149: floor(149/3) = 49, floor(149/5) = 29
M1 Counts multiples of 15 (both) = floor(149/15) = 9 and combines correctly, e.g. (49 - 9) + (29 - 9), oe
A1 60 cao
Answer: 60

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Factors and Multiples: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

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1.11DB Factors and Multiples: Fluency and Exam Drill (Part 2)

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